%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP573-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:27:34 PM UTC 2026
% Result : Unsatisfiable 4.80s 1.12s
% Output : CNFRefutation 4.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of clauses : 30 ( 30 unt; 0 nHn; 9 RR)
% Number of literals : 30 ( 29 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t2,axiom,
double_divide(double_divide(X1,X2),identity) = multiply(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t0,axiom,
double_divide(X1,identity) = inverse(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t7,plain,
double_divide(X1,identity) = inverse(X1),
inference(orient,[status(thm)],[t0]) ).
cnf(t210,plain,
inverse(double_divide(X1,X2)) = multiply(X2,X1),
inference(step,[status(thm)],[t2,t7]) ).
cnf(t10,plain,
inverse(double_divide(X1,X2)) = multiply(X2,X1),
inference(orient,[status(thm)],[t210]) ).
cnf(t1,axiom,
double_divide(X1,inverse(X1)) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t9,plain,
double_divide(X1,inverse(X1)) = identity,
inference(orient,[status(thm)],[t1]) ).
cnf(t12,plain,
multiply(inverse(X1),X1) = inverse(identity),
inference(cp,[status(thm)],[t10,t9]) ).
cnf(t18,plain,
multiply(inverse(X1),X1) = inverse(identity),
inference(orient,[status(thm)],[t12]) ).
cnf(t3,axiom,
double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X3,X1)),double_divide(X3,identity))),double_divide(identity,identity)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t4,plain,
double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X3,X1)),double_divide(X3,identity))),double_divide(identity,identity)) = X2,
inference(orient,[status(thm)],[t3]) ).
cnf(t208,plain,
double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X3,X1)),inverse(X3))),double_divide(identity,identity)) = X2,
inference(step,[status(thm)],[t4,t7]) ).
cnf(t209,plain,
double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X3,X1)),inverse(X3))),inverse(identity)) = X2,
inference(step,[status(thm)],[t208,t7]) ).
cnf(t8,plain,
double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X3,X1)),inverse(X3))),inverse(identity)) = X2,
inference(rw,[status(thm)],[t209]) ).
cnf(t69,plain,
double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X3,X1)),inverse(X3))),inverse(identity)) = X2,
inference(orient,[status(thm)],[t8]) ).
cnf(t70,plain,
X1 = double_divide(double_divide(identity,double_divide(double_divide(X1,inverse(X2)),inverse(X2))),inverse(identity)),
inference(cp,[status(thm)],[t69,t7]) ).
cnf(t137,plain,
double_divide(double_divide(identity,double_divide(double_divide(X1,inverse(X2)),inverse(X2))),inverse(identity)) = X1,
inference(orient,[status(thm)],[t70]) ).
cnf(t138,plain,
X1 = double_divide(double_divide(identity,double_divide(identity,inverse(X1))),inverse(identity)),
inference(cp,[status(thm)],[t137,t9]) ).
cnf(t155,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(X1))),inverse(identity)) = X1,
inference(orient,[status(thm)],[t138]) ).
cnf(t156,plain,
identity = double_divide(double_divide(identity,identity),inverse(identity)),
inference(cp,[status(thm)],[t155,t9]) ).
cnf(t215,plain,
identity = double_divide(inverse(identity),inverse(identity)),
inference(step,[status(thm)],[t156,t7]) ).
cnf(t167,plain,
double_divide(inverse(identity),inverse(identity)) = identity,
inference(orient,[status(thm)],[t215]) ).
cnf(t175,plain,
inverse(identity) = double_divide(double_divide(identity,double_divide(identity,inverse(identity))),inverse(identity)),
inference(cp,[status(thm)],[t137,t167]) ).
cnf(t216,plain,
inverse(identity) = identity,
inference(step,[status(thm)],[t175,t155]) ).
cnf(t176,plain,
inverse(identity) = identity,
inference(orient,[status(thm)],[t216]) ).
cnf(t217,plain,
multiply(inverse(X1),X1) = identity,
inference(step,[status(thm)],[t18,t176]) ).
cnf(t177,plain,
multiply(inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t217]) ).
cnf(goal_0,negated_conjecture,
multiply(inverse(a1),a1) != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
identity != identity,
inference(rw,[status(thm)],[goal_0,t177]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP573-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 15:11:25 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.80/1.12 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.80/1.12 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------